Finite Group Databasebeta

Subgroups — #22548784

Order 8034.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16860816	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₁₃×C₁₀₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₃×C₁₀₃	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₂×C₁₀₃⋊C₃	—	13	1	no	maximal, Hall
5	C₁₀₃⋊C₃	—	13	1	no	Hall
6	C₂×C₁₀₃	—	13	1	no	Hall
7	C₁₀₃	D₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
8	D₁₃⋊C₃	—	103	1	no	maximal, Hall
9	C₁₃⋊C₃	—	103	1	no	Hall
10	D₁₃	C₁₀₃⋊C₃	1	1	yes	characteristic, complemented, Hall
11	C₁₃	C₂×C₁₀₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
12	C₂×C₃	—	1339	1	no	Hall
13	C₃	—	1339	1	no	Sylow
14	C₂	—	13	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₁₃×C₁₀₃	C₂×C₃
LCS	G ▷ C₁₃×C₁₀₃
UCS	C₁

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. #16860816	C₂	semidirect
2. D₁₃×C₁₀₃	C₃	semidirect
3. C₁₃×C₁₀₃	C₂×C₃	semidirect
7. C₁₀₃	D₁₃⋊C₃	semidirect
10. D₁₃	C₁₀₃⋊C₃	semidirect
11. C₁₃	C₂×C₁₀₃⋊C₃	semidirect